A conventional paper core used in a thin material sheet winding mechanism is conveyed to a location beside a first roller by a conveyor and is then forced into a curved guiding passage by a push plate. The paper core, after reaching a winding nip through the curved guiding passage, receives a thin material sheet wound thereon to form a roll, such as a toilet paper roll and a kitchen towel roll. When it is about to complete to roll, a rotary bar is controlled to have a relative speed thereof with respect to the first winding roller become faster or slower to induce a speed difference, which may break or tear the thin material sheet. Or alternatively, a cutting device is employed to directly cut off the thin material sheet.